ANOVA and ChiSq Survey Assignment

Statistical Tests

Heather Bierman

Fairleigh Dickinson

DSCI_6600_81 Business Analytics

Zhaobo Wang

October 30, 2021

Executive Summary

ANOVA test refers to a statistical test used to test any statistical differences between any two or more independent groups. The groups being tested can be of people, things, elements, etc. various types of ANOVA tests can be done, including the one way, two ways, among others. Like the t test, the ANOVA test works through the analysis of the various levels of variances within two or more groups by the samples taken from every group.

In the groups that are to be studied, if much variance exists, then it means that there are more chances that the average of the selected sample from the data would be different as a result of chance. Note that the variance is the spread of the entailed information from the average value. ANOVA takes into consideration the sample size and the existing differences of the samples that are being sued in the study. All the involved elements are then put together into an f value that can be analyzed to produce a probability.

From the ANOVA done on the given assignment, there are various findings. Firstly, the p value is 0.93272 in the first test, which is greater than 0.05, showing no statistical significance between the groups involved. In the second test, the value is 0.00055, which is less than 0.05, which shows possible differences because the value is less than 0.05. Nevertheless, there seems to be similarities in the coffee and t shirt elements of the above. In the third test, the p value is 0.101783, which is more than the alpha value of 0.05; hence, there seem to be no differences between the groups in the study.

In general, it is evident that the first and the third tests show a lack of any differences in the groups of study. The second one shows the existence of the differences as explained above. As mentioned above, the ANOVA test has helped us study the groups of study and try to evaluate if there are any differences between them.

Part 1: Hypothesis Testing 1

From the first ANOVA test, it is evident that there is no significant difference in the groups presented. The p value is 0.93272, and it is evident that it exceeds the 0.05 alpha levels. It means that the result has no statistical significance. In essence, we can conclude that the groups have no significant differences between them.

Part 2: Hypothesis testing 2

From the ANOVA test, it is evident that 0.00055 is the p value. It is less than the 0.05 alpha levels. It points out the possible existing differences between the group values. When looking keenly at the values, we get that there seem to be similarities in the above coffee and t shirt elements. The difference between the value and 0.05 shows the extent of the similarities between the elements in question.

Part 3: Hypothesis testing 3

In part 3, i.e. the demographical elements, the p value of the ANOVA test is 0.101783, which is simply more than 0.05. It, therefore, points to the lack of any significant differences between the elements in discussion in part 3.

The above discussion and the calculations show that the groups selected are random, and indeed there are no significant differences between them. The ANOVA tests help to find out the samples used and how the various characteristics can be evaluated and studied between them. It means that the study silences the critics who may have untested or unverified conclusions. For instance, the groups have significant differences because they are randomly selected, yet they don’t.